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Cyclic creep and fracture of a Cu–SiO2 bicrystal at an intermediate temperature of 673 K
Materials Science and Engineering A 510–511 (2009) 413–416
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Cyclic creep and fracture of a Cu–SiO2 bicrystal at an intermediate temperature of 673 K H. Miura a,∗ , T. Sakai a , M. Kato b a b
Department of Mechanical Engineering and Intelligent Systems, UEC Tokyo (The University of Electro-Communications), Chofu, Tokyo 182-8585, Japan Department of Materials Science and Engineering, Tokyo Institute of Technology, 4259-J2-60 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan
a r t i c l e
i n f o
Article history: Received 20 November 2007 Received in revised form 25 March 2008 Accepted 3 April 2008 Keywords: Cu–SiO2 alloy Bicrystal Creep Grain boundary Grain-boundary sliding
a b s t r a c t Cyclic creep and fracture behavior at 673 K of orientation-controlled Cu–SiO2 bicrystals with [0 0 1] twist 20◦ grain boundaries was investigated. The cyclic creep and life depended on both the stress amplitude and the frequency of the cyclic load. Most bicrystals fractured intergranularly. The number of cycles to failure shortened drastically with decreasing the frequency and with increasing the stress amplitude, while the time to failure remained nearly the same irrespective of the frequency. Since the cyclic creep life was controlled by the occurrence of grain-boundary fracture, the above observations can be understood reasonably by considering stress concentration and void formation at grain-boundary SiO2 particles. When grain-boundary sliding takes place, the particles impede the sliding and the stress concentration sites are created. This causes the intergranular fracture and controls the cyclic creep life. © 2008 Elsevier B.V. All rights reserved.
1. Introduction It is well known that grain-boundary sliding (GBS) lowers creep strength and life (i.e., the time to rupture) [1]. Second-phase particles dispersed on grain boundaries can effectively suppress GBS [2–4]. The particles contribute also to the impediment of the grainboundary migration [5] and to lowering the mobility of dislocations. The dispersed particles, however, sometimes enhance the grainboundary cracking (GBC) and cause the intergranular fracture. The suppression of GBS by the grain-boundary particles induces severe stress concentration sites at particle/matrix interfaces [3,4] and the concentrated stress can become higher than the fracture stress [4]. The resultant occurrence of GBC causes significant shortening of creep life. GBC is, therefore, one of the most important life controlling factors in the dispersion-hardened alloys during hightemperature deformation. The dispersion-hardened alloys are sometimes subjected to cyclic creep or fatigue conditions at elevated temperatures. Miura et al. [6] have performed experiments and shown that grainboundary character dependence of cracking and discontinuous life shortening, i.e., abrupt decrease in the number of cycles to failure, by GBC from the experiments using orientation-controlled Cu–SiO2 bicrystals. They have concluded that the life of polycrystalline dispersion-hardened metallic materials during cyclic
∗ Corresponding author. Tel.: +81 42 443 5409; fax: +81 42 484 3327. E-mail address: [email protected] (H. Miura). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.04.119
creep is determined by an easy occurrence of GBC at special grain boundaries. However, investigations on cyclic creep behavior of dispersionhardened alloys are rather limited [6,7]. The present study investigates the effect of cyclic frequency on cyclic creep and fracture behavior. All specimens were taken from the same orientation-controlled Cu bicrystal with dispersed SiO2 particles to avoid the effect of grain-boundary character dependence of the cyclic creep behavior in polycrystalline materials. 2. Experimental procedures A Cu–0.2 mass%Si alloy bicrystal of 2 mm in thickness, having a [0 0 1] twist 20◦ boundary, was grown by the Bridgman method using seed crystals. The [0 0 1] twist 20◦ boundary is known to slide relatively easily [8]. The bicrystal was internally oxidized by the powder pack method with a mixture of Cu (1 part), Cu2 O (1 part) and Al2 O3 (2 parts) at 1273 K for 24 h. By this treatment, we have obtained dispersed SiO2 particles (1.7% volume fraction) in a Cu matrix. The average particle radii, r, dispersed in the matrix and on the grain boundary were about 95 and 160 nm, respectively. To eliminate excess oxygen, a degassing treatment at 1273 K for 24 h in a graphite mold in vacuum was performed. Specimens of 12 mm gage length and 4 mm × 2 mm cross section, in which grain boundaries were inclined 45◦ with respect to the loading direction, were cut by electric discharge machining. After mirror-like finishing of the surfaces by mechanical and electrical polishing, they were cyclically crept at 673 K in vacuum of
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Fig. 1. Strain vs. number of cycle curves of the bicrystal cyclically crept at 673 K and at (a) f = 1 Hz and (b) f = 20 Hz. The insets show stress-amplitude values.
Table 1 Mechanical properties of the Cu–SiO2 bicrystal when tensile tested at 673 K. Yield stress (MPa) Work hardening rate (d/dε) Fracture stress (MPa) Fracture strain
27.2 183 76.6 0.265
about 10−3 Pa in a servo-hydraulic machine. Tensile–tensile cyclic loading with load ratio of 0.1 was applied at frequency between 1 and 100 Hz. Here, the load ratio R and stress amplitude a are defined using applied maximum stress max and minimum stress min as follows. R=
min max
a =
max − min 2
(1) (2)
After the tests, the microstructure was observed using scanning electron microscopy (SEM). Mechanical characteristics of the Cu–SiO2 bicrystal sample, obtained by tensile test at 673 K and at an initial strain rate of 4.2 × 10−4 s−1 , are summarized in Table 1. The work hardening rate in Table 1 is taken from the slope of the true stress vs. true strain curve just after yielding. 3. Results and discussion 3.1. Cyclic creep behavior Fig. 1 shows a series of curves of strain against cyclic number (the ε–N curves) at f = 1 Hz and 20 Hz. The insets indicate stress-
amplitude values. The curves in Fig. 1 show almost linear increase of the strain during earlier cycles and the strain increment per cycle ε becomes very large before the rupture. The strain at a fixed number of cycle increases with increasing applied stress amplitude. The maximum stress max when cyclically crept at a = 15 MPa is about 33 MPa. Though this is the lowest stress amplitude in the present study, the value of 33 MPa is higher than the yield stress (see Table 1). The increase of strain is, therefore, mainly due to plastic deformation. Fig. 1 demonstrates that ε depends strongly on the cyclic frequency. The average strain per cycle εav and the average strain rate till rupture were calculated from the ε–N curves, and the results are summarized in Fig. 2. It is found that εav increases with increasing stress amplitude and with decreasing frequency and that εav at f = 1 Hz is more than one order of magnitude larger than that at f = 100 Hz irrespective of the stress amplitude. The dependency of εav on the stress amplitude should reflect the difference in the amount of plastic deformation of the matrix rather than the difference in the amount of GBS. This is because, as will be shown later, the total amount of GBS till rupture is estimated to be less than 10 m (see Fig. 5). Moreover, the origin of the strong dependency of εav on the stress amplitude a is believed to be caused by large difference in the duration of the creep deformation. This is supported by the fact that the average strain rate does not depend strongly on the frequency f (Fig. 2(b)). Therefore, the dominant factors to determine the amount of strain during cyclic creep at a fixed temperature is identified to be the duration of cyclic deformation and stress amplitude. Fig. 3 shows the stress amplitude-life to rupture (S–Nf ) and stress amplitude-time to rupture (S–tf ) curves for the all the samples
Fig. 2. Changes in (a) the average (from the onset of cyclic creep till rupture) strain per cycle and (b) the average strain rate when cyclically crept at various frequencies at 673 K.
H. Miura et al. / Materials Science and Engineering A 510–511 (2009) 413–416
415
Fig. 3. (a) S–Nf curves at 673 K when crept at various frequencies. Solid and open symbols indicate transgranular and intergranular fracture, respectively. (b) is the replot of (a) as a function of cyclic creep time tf .
Fig. 4. (a) Photograph of the grain-boundary area after creep at T = 673 K, f = 20 Hz, a = 15 MPa to N = 103 cycles. (b) is the magnified view of the area indicated by dotted lines in (a).
tested. Most bicrystals fractured intergranularly. It is evident, therefore, that the number of cycles and the time to failure are controlled by the occurrence of grain-boundary fracture. The number of cycles to failure (Nf ) becomes shorter with increasing stress amplitude and decreasing frequency (Fig. 3(a)). In spite of the above results, the time to failure (tf ) is not so much different irrespective of frequency (Fig. 3(b)). 3.2. Surface morphology and fractography GBC starting from the specimen surface during cyclic creep was observed using SEM. Some of the creep tests were interrupted before rupture and a typical region near the grain-boundary area
is shown in Fig. 4. Although cyclically crept only to N = 103 , which is smaller than 1/10 of the life, cracks already appeared along the grain boundary (Fig. 4(a)) and voids were nucleated at the edges of the lenticular-shaped grain-boundary SiO2 particles (Fig. 4(b)). It is known that GBS occurs extensively when the bicrystal is deformed at 673 K [8]. In such a case, the SiO2 particles impede the sliding and cause severe stress concentrations. Fig. 5 shows the grain-boundary fracture surface after cyclic creep at f = 20 Hz and a = 15 MPa. All the fracture surfaces were of mixed character with elongated voids (Fig. 5(a)) and dimples (Fig. 5(b)) which suggest the occurrence of brittle intergranular and ductile intergranular fracture, respectively. The elongated voids must have been formed when SiO2 particles are displaced by GBS
Fig. 5. Complicated feature of the grain-boundary fractured surface. The feature of the fracture surface varies place to place. The sample was crept at T = 673 K, f = 20 Hz, a = 15 MPa to failure.
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H. Miura et al. / Materials Science and Engineering A 510–511 (2009) 413–416
[3,4]. This suggests that the particles could not fully suppress GBS due to quite high stress concentrations generated near the particles. In fact, the concentrated stress is calculated to be possibly as large as 270 MPa [4], which is much higher than the fracture stress (see Table 1). The length of the elongated voids, at most about 10 m, shows the amount of GBS until rupture (Nf = 1.7 × 104 ). Dimples in Fig. 5(b) were most probably formed at the final stage of rupture. Although the void formation is caused by GBS blocked by SiO2 particles, it must also be affected by the work hardening of the Cu matrix. When the matrix exhibits pronounced work hardening, particle dragging to form elongated voids may become rather difficult. The void length formed at N = 103 was about 0.5 m (Fig. 4), while that at N = 1.7 × 104 was about 10 m. Therefore, it is reasonable to consider that the elongated voids have grown almost proportionally to the number of cycles. That is, GBS and the resultant stress concentrations around the grain-boundary particles must have controlled the void formation and growth. After the formation of elongated voids, crack propagated along the grain boundary and, then, finally caused intergranular fracture. 3.3. Formation of stress concentration by GBS and effect of relaxation By the impediment of GBS, severe stress concentration sites appear at the edges of the grain-boundary particles. This concentrated stress acts as a back stress to stop GBS and, as a result, GBS occurs only until it reaches a certain saturated amount. The kinetics of GBS with grain-boundary particles has been studied [9]. Necessary time for attaining the saturated GBS for the [0 0 1] twist 20◦ grain boundary in a Cu–1.7 vol.%SiO2 alloy has been estimated to be less than 10−3 s−1 at 673 K [9]. This means that the saturated GBS and, therefore, stress concentrations are soon developed before the duration of one-cycle creep at all the testing conditions in the present study. As mentioned above, the concentrated stress is much higher than the fracture strength [4]. Therefore, the void formation at the edges of the particles can be understood reasonably. On the other hand, such stress concentrations can be relaxed if the particle/matrix interfacial diffusion is well operative [10]. If this is the case, it is difficult to justify the void nucleation and the above discussion becomes invalid. The characteristic time for the relaxation by interfacial diffusion, P , depends on the particle size and temperature as [10]. P =
20 1 − kTr 3 2
7 − 5v
DW˝
(3)
Here, is Poisson’s ratio, k the Boltzmann’s constant, T the temperature, the shear modulus, D the interfacial (particle/matrix) diffusivity, W the thickness of the particle/matrix interface, and ˝ the atomic volume. Using D = 1.1 × 10−2 T exp(−2.5 × 10−19 J/kT) [10], W = 2.5 × 10−10 m and 160 nm for grain-boundary particles, the value of P at 673 K is estimated as p = 3 s. Since the slowest cyclic creep frequency employed in the present study is 1 Hz and
the calculated p is longer than 1 s, the stress concentration formed around the grain-boundary particle cannot be fully relaxed during the unloading periods of the cyclic creep. Therefore, the impediment of GBS necessarily results in the nucleation of voids and cracks at all the testing conditions in the present study. This accounts for the occurrence of intergranular fracture. At sufficiently high temperatures or at very low frequencies, the stresses caused by the particle-blocked sliding can be fully relaxed by the particle/matrix interfacial diffusion process. In that case, GBCs become difficult to be formed [3]. Recovery in the matrix by lattice diffusion would also affect softening, though the process is two orders of magnitude slower than that by interfacial diffusion [10,11]. Therefore, we can reasonably conclude that the stress concentrations that developed just at the beginning of cyclic creep cannot be fully relaxed and should cause void formation around the particles (Fig. 4). The applied shear stress on the grain boundary would induce the dragging of the grain-boundary particles and the elongated voids are formed. The evolution of the elongated voids and their coalescence finally leads to the initiation of GBC. Since GBS is assumed to be diffusion controlled [1], the time to failure at a fixed stress amplitude and temperature must be essentially independent of the cyclic frequency of deformation. 4. Summary The current investigations yield the following results. (i) Cyclic creep of dispersion-hardened alloy at intermediate temperature causes intergranular fracture. (ii) While the number of cycles to failure becomes shorter with increasing stress amplitude and with decreasing cyclic frequency, the time to fracture is independent of frequency. (iii) The cyclic creep and fracture behavior could be understood reasonably by considering the effects of grain-boundary SiO2 particles on the blockage of grain-boundary sliding. Stress concentration sites developed at the grain-boundary particles induce formation of voids and cracks at the particles. This causes the grain-boundary fracture and controlled the cyclic creep life. References [1] R. Raj, M.F. Ashby, Metall. Trans. 2 (1971) 1113–1127. [2] T. Mori, Proceedings Eshelby Memorial Symposium, Cambridge University Press, 1985, pp. 277–291. [3] H. Miura, T. Sakai, N. Tada, M. Kato, T. Mori, Acta Metall. Mater. 41 (1993) 1207–1213. [4] H. Miura, T. Sakai, H. Toda, Acta Mater. 51 (2003) 4707–4717. [5] A.P. Manohar, M. Ferry, T. Chandra, ISIJ Int. 38 (1998) 913–924. [6] H. Miura, T. Sakai, M. Kato, Int. J. Fatigue 24 (2002) 943–948. [7] M.W. Stobbs, F.D. Watt, M.L. Brown, Phil. Mag. 23 (1971) 1169–1184. [8] R. Monzen, T. Suzuki, Phil. Mag. Lett. 74 (1996) 9–15. [9] H. Miura, T. Sakai, N. Tada, M. Kato, Phil. Mag. A 73 (1996) 871–882. [10] T. Mori, M. Okabe, T. Mura, Acta Metall. 28 (1980) 319–325. [11] N. Shigenaka, M. Koda, T. Mori, Scripta Metall. 17 (1983) 1021–1022.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Cyclic creep and fracture of a Cu–SiO2 bicrystal at an intermediate temperature of 673 K H. Miura a,∗ , T. Sakai a , M. Kato b a b
Department of Mechanical Engineering and Intelligent Systems, UEC Tokyo (The University of Electro-Communications), Chofu, Tokyo 182-8585, Japan Department of Materials Science and Engineering, Tokyo Institute of Technology, 4259-J2-60 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan
a r t i c l e
i n f o
Article history: Received 20 November 2007 Received in revised form 25 March 2008 Accepted 3 April 2008 Keywords: Cu–SiO2 alloy Bicrystal Creep Grain boundary Grain-boundary sliding
a b s t r a c t Cyclic creep and fracture behavior at 673 K of orientation-controlled Cu–SiO2 bicrystals with [0 0 1] twist 20◦ grain boundaries was investigated. The cyclic creep and life depended on both the stress amplitude and the frequency of the cyclic load. Most bicrystals fractured intergranularly. The number of cycles to failure shortened drastically with decreasing the frequency and with increasing the stress amplitude, while the time to failure remained nearly the same irrespective of the frequency. Since the cyclic creep life was controlled by the occurrence of grain-boundary fracture, the above observations can be understood reasonably by considering stress concentration and void formation at grain-boundary SiO2 particles. When grain-boundary sliding takes place, the particles impede the sliding and the stress concentration sites are created. This causes the intergranular fracture and controls the cyclic creep life. © 2008 Elsevier B.V. All rights reserved.
1. Introduction It is well known that grain-boundary sliding (GBS) lowers creep strength and life (i.e., the time to rupture) [1]. Second-phase particles dispersed on grain boundaries can effectively suppress GBS [2–4]. The particles contribute also to the impediment of the grainboundary migration [5] and to lowering the mobility of dislocations. The dispersed particles, however, sometimes enhance the grainboundary cracking (GBC) and cause the intergranular fracture. The suppression of GBS by the grain-boundary particles induces severe stress concentration sites at particle/matrix interfaces [3,4] and the concentrated stress can become higher than the fracture stress [4]. The resultant occurrence of GBC causes significant shortening of creep life. GBC is, therefore, one of the most important life controlling factors in the dispersion-hardened alloys during hightemperature deformation. The dispersion-hardened alloys are sometimes subjected to cyclic creep or fatigue conditions at elevated temperatures. Miura et al. [6] have performed experiments and shown that grainboundary character dependence of cracking and discontinuous life shortening, i.e., abrupt decrease in the number of cycles to failure, by GBC from the experiments using orientation-controlled Cu–SiO2 bicrystals. They have concluded that the life of polycrystalline dispersion-hardened metallic materials during cyclic
∗ Corresponding author. Tel.: +81 42 443 5409; fax: +81 42 484 3327. E-mail address: [email protected] (H. Miura). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.04.119
creep is determined by an easy occurrence of GBC at special grain boundaries. However, investigations on cyclic creep behavior of dispersionhardened alloys are rather limited [6,7]. The present study investigates the effect of cyclic frequency on cyclic creep and fracture behavior. All specimens were taken from the same orientation-controlled Cu bicrystal with dispersed SiO2 particles to avoid the effect of grain-boundary character dependence of the cyclic creep behavior in polycrystalline materials. 2. Experimental procedures A Cu–0.2 mass%Si alloy bicrystal of 2 mm in thickness, having a [0 0 1] twist 20◦ boundary, was grown by the Bridgman method using seed crystals. The [0 0 1] twist 20◦ boundary is known to slide relatively easily [8]. The bicrystal was internally oxidized by the powder pack method with a mixture of Cu (1 part), Cu2 O (1 part) and Al2 O3 (2 parts) at 1273 K for 24 h. By this treatment, we have obtained dispersed SiO2 particles (1.7% volume fraction) in a Cu matrix. The average particle radii, r, dispersed in the matrix and on the grain boundary were about 95 and 160 nm, respectively. To eliminate excess oxygen, a degassing treatment at 1273 K for 24 h in a graphite mold in vacuum was performed. Specimens of 12 mm gage length and 4 mm × 2 mm cross section, in which grain boundaries were inclined 45◦ with respect to the loading direction, were cut by electric discharge machining. After mirror-like finishing of the surfaces by mechanical and electrical polishing, they were cyclically crept at 673 K in vacuum of
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H. Miura et al. / Materials Science and Engineering A 510–511 (2009) 413–416
Fig. 1. Strain vs. number of cycle curves of the bicrystal cyclically crept at 673 K and at (a) f = 1 Hz and (b) f = 20 Hz. The insets show stress-amplitude values.
Table 1 Mechanical properties of the Cu–SiO2 bicrystal when tensile tested at 673 K. Yield stress (MPa) Work hardening rate (d/dε) Fracture stress (MPa) Fracture strain
27.2 183 76.6 0.265
about 10−3 Pa in a servo-hydraulic machine. Tensile–tensile cyclic loading with load ratio of 0.1 was applied at frequency between 1 and 100 Hz. Here, the load ratio R and stress amplitude a are defined using applied maximum stress max and minimum stress min as follows. R=
min max
a =
max − min 2
(1) (2)
After the tests, the microstructure was observed using scanning electron microscopy (SEM). Mechanical characteristics of the Cu–SiO2 bicrystal sample, obtained by tensile test at 673 K and at an initial strain rate of 4.2 × 10−4 s−1 , are summarized in Table 1. The work hardening rate in Table 1 is taken from the slope of the true stress vs. true strain curve just after yielding. 3. Results and discussion 3.1. Cyclic creep behavior Fig. 1 shows a series of curves of strain against cyclic number (the ε–N curves) at f = 1 Hz and 20 Hz. The insets indicate stress-
amplitude values. The curves in Fig. 1 show almost linear increase of the strain during earlier cycles and the strain increment per cycle ε becomes very large before the rupture. The strain at a fixed number of cycle increases with increasing applied stress amplitude. The maximum stress max when cyclically crept at a = 15 MPa is about 33 MPa. Though this is the lowest stress amplitude in the present study, the value of 33 MPa is higher than the yield stress (see Table 1). The increase of strain is, therefore, mainly due to plastic deformation. Fig. 1 demonstrates that ε depends strongly on the cyclic frequency. The average strain per cycle εav and the average strain rate till rupture were calculated from the ε–N curves, and the results are summarized in Fig. 2. It is found that εav increases with increasing stress amplitude and with decreasing frequency and that εav at f = 1 Hz is more than one order of magnitude larger than that at f = 100 Hz irrespective of the stress amplitude. The dependency of εav on the stress amplitude should reflect the difference in the amount of plastic deformation of the matrix rather than the difference in the amount of GBS. This is because, as will be shown later, the total amount of GBS till rupture is estimated to be less than 10 m (see Fig. 5). Moreover, the origin of the strong dependency of εav on the stress amplitude a is believed to be caused by large difference in the duration of the creep deformation. This is supported by the fact that the average strain rate does not depend strongly on the frequency f (Fig. 2(b)). Therefore, the dominant factors to determine the amount of strain during cyclic creep at a fixed temperature is identified to be the duration of cyclic deformation and stress amplitude. Fig. 3 shows the stress amplitude-life to rupture (S–Nf ) and stress amplitude-time to rupture (S–tf ) curves for the all the samples
Fig. 2. Changes in (a) the average (from the onset of cyclic creep till rupture) strain per cycle and (b) the average strain rate when cyclically crept at various frequencies at 673 K.
H. Miura et al. / Materials Science and Engineering A 510–511 (2009) 413–416
415
Fig. 3. (a) S–Nf curves at 673 K when crept at various frequencies. Solid and open symbols indicate transgranular and intergranular fracture, respectively. (b) is the replot of (a) as a function of cyclic creep time tf .
Fig. 4. (a) Photograph of the grain-boundary area after creep at T = 673 K, f = 20 Hz, a = 15 MPa to N = 103 cycles. (b) is the magnified view of the area indicated by dotted lines in (a).
tested. Most bicrystals fractured intergranularly. It is evident, therefore, that the number of cycles and the time to failure are controlled by the occurrence of grain-boundary fracture. The number of cycles to failure (Nf ) becomes shorter with increasing stress amplitude and decreasing frequency (Fig. 3(a)). In spite of the above results, the time to failure (tf ) is not so much different irrespective of frequency (Fig. 3(b)). 3.2. Surface morphology and fractography GBC starting from the specimen surface during cyclic creep was observed using SEM. Some of the creep tests were interrupted before rupture and a typical region near the grain-boundary area
is shown in Fig. 4. Although cyclically crept only to N = 103 , which is smaller than 1/10 of the life, cracks already appeared along the grain boundary (Fig. 4(a)) and voids were nucleated at the edges of the lenticular-shaped grain-boundary SiO2 particles (Fig. 4(b)). It is known that GBS occurs extensively when the bicrystal is deformed at 673 K [8]. In such a case, the SiO2 particles impede the sliding and cause severe stress concentrations. Fig. 5 shows the grain-boundary fracture surface after cyclic creep at f = 20 Hz and a = 15 MPa. All the fracture surfaces were of mixed character with elongated voids (Fig. 5(a)) and dimples (Fig. 5(b)) which suggest the occurrence of brittle intergranular and ductile intergranular fracture, respectively. The elongated voids must have been formed when SiO2 particles are displaced by GBS
Fig. 5. Complicated feature of the grain-boundary fractured surface. The feature of the fracture surface varies place to place. The sample was crept at T = 673 K, f = 20 Hz, a = 15 MPa to failure.
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H. Miura et al. / Materials Science and Engineering A 510–511 (2009) 413–416
[3,4]. This suggests that the particles could not fully suppress GBS due to quite high stress concentrations generated near the particles. In fact, the concentrated stress is calculated to be possibly as large as 270 MPa [4], which is much higher than the fracture stress (see Table 1). The length of the elongated voids, at most about 10 m, shows the amount of GBS until rupture (Nf = 1.7 × 104 ). Dimples in Fig. 5(b) were most probably formed at the final stage of rupture. Although the void formation is caused by GBS blocked by SiO2 particles, it must also be affected by the work hardening of the Cu matrix. When the matrix exhibits pronounced work hardening, particle dragging to form elongated voids may become rather difficult. The void length formed at N = 103 was about 0.5 m (Fig. 4), while that at N = 1.7 × 104 was about 10 m. Therefore, it is reasonable to consider that the elongated voids have grown almost proportionally to the number of cycles. That is, GBS and the resultant stress concentrations around the grain-boundary particles must have controlled the void formation and growth. After the formation of elongated voids, crack propagated along the grain boundary and, then, finally caused intergranular fracture. 3.3. Formation of stress concentration by GBS and effect of relaxation By the impediment of GBS, severe stress concentration sites appear at the edges of the grain-boundary particles. This concentrated stress acts as a back stress to stop GBS and, as a result, GBS occurs only until it reaches a certain saturated amount. The kinetics of GBS with grain-boundary particles has been studied [9]. Necessary time for attaining the saturated GBS for the [0 0 1] twist 20◦ grain boundary in a Cu–1.7 vol.%SiO2 alloy has been estimated to be less than 10−3 s−1 at 673 K [9]. This means that the saturated GBS and, therefore, stress concentrations are soon developed before the duration of one-cycle creep at all the testing conditions in the present study. As mentioned above, the concentrated stress is much higher than the fracture strength [4]. Therefore, the void formation at the edges of the particles can be understood reasonably. On the other hand, such stress concentrations can be relaxed if the particle/matrix interfacial diffusion is well operative [10]. If this is the case, it is difficult to justify the void nucleation and the above discussion becomes invalid. The characteristic time for the relaxation by interfacial diffusion, P , depends on the particle size and temperature as [10]. P =
20 1 − kTr 3 2
7 − 5v
DW˝
(3)
Here, is Poisson’s ratio, k the Boltzmann’s constant, T the temperature, the shear modulus, D the interfacial (particle/matrix) diffusivity, W the thickness of the particle/matrix interface, and ˝ the atomic volume. Using D = 1.1 × 10−2 T exp(−2.5 × 10−19 J/kT) [10], W = 2.5 × 10−10 m and 160 nm for grain-boundary particles, the value of P at 673 K is estimated as p = 3 s. Since the slowest cyclic creep frequency employed in the present study is 1 Hz and
the calculated p is longer than 1 s, the stress concentration formed around the grain-boundary particle cannot be fully relaxed during the unloading periods of the cyclic creep. Therefore, the impediment of GBS necessarily results in the nucleation of voids and cracks at all the testing conditions in the present study. This accounts for the occurrence of intergranular fracture. At sufficiently high temperatures or at very low frequencies, the stresses caused by the particle-blocked sliding can be fully relaxed by the particle/matrix interfacial diffusion process. In that case, GBCs become difficult to be formed [3]. Recovery in the matrix by lattice diffusion would also affect softening, though the process is two orders of magnitude slower than that by interfacial diffusion [10,11]. Therefore, we can reasonably conclude that the stress concentrations that developed just at the beginning of cyclic creep cannot be fully relaxed and should cause void formation around the particles (Fig. 4). The applied shear stress on the grain boundary would induce the dragging of the grain-boundary particles and the elongated voids are formed. The evolution of the elongated voids and their coalescence finally leads to the initiation of GBC. Since GBS is assumed to be diffusion controlled [1], the time to failure at a fixed stress amplitude and temperature must be essentially independent of the cyclic frequency of deformation. 4. Summary The current investigations yield the following results. (i) Cyclic creep of dispersion-hardened alloy at intermediate temperature causes intergranular fracture. (ii) While the number of cycles to failure becomes shorter with increasing stress amplitude and with decreasing cyclic frequency, the time to fracture is independent of frequency. (iii) The cyclic creep and fracture behavior could be understood reasonably by considering the effects of grain-boundary SiO2 particles on the blockage of grain-boundary sliding. Stress concentration sites developed at the grain-boundary particles induce formation of voids and cracks at the particles. This causes the grain-boundary fracture and controlled the cyclic creep life. References [1] R. Raj, M.F. Ashby, Metall. Trans. 2 (1971) 1113–1127. [2] T. Mori, Proceedings Eshelby Memorial Symposium, Cambridge University Press, 1985, pp. 277–291. [3] H. Miura, T. Sakai, N. Tada, M. Kato, T. Mori, Acta Metall. Mater. 41 (1993) 1207–1213. [4] H. Miura, T. Sakai, H. Toda, Acta Mater. 51 (2003) 4707–4717. [5] A.P. Manohar, M. Ferry, T. Chandra, ISIJ Int. 38 (1998) 913–924. [6] H. Miura, T. Sakai, M. Kato, Int. J. Fatigue 24 (2002) 943–948. [7] M.W. Stobbs, F.D. Watt, M.L. Brown, Phil. Mag. 23 (1971) 1169–1184. [8] R. Monzen, T. Suzuki, Phil. Mag. Lett. 74 (1996) 9–15. [9] H. Miura, T. Sakai, N. Tada, M. Kato, Phil. Mag. A 73 (1996) 871–882. [10] T. Mori, M. Okabe, T. Mura, Acta Metall. 28 (1980) 319–325. [11] N. Shigenaka, M. Koda, T. Mori, Scripta Metall. 17 (1983) 1021–1022.